HW2 solutions - STAT 2004 Homework 2 Solutions Obs(i 1 2 3...

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STAT 2004 Homework 2 Solutions Obs (i) X Y X 2 Y 2 XY 1 1935 32.1 3744225 1031.4 1 62113.5 2 1940 30.5 9763600 960.25 59170.5 3 1945 24.4 3783025 595.36 47458.0 4 1950 23.0 3802500 529.00 448500.0 5 1955 19.1 3822025 364.81 37340.5 6 1960 15.6 3841600 243.36 30576.0 7 1965 12.4 3861225 153.76 24366.0 8 1970 9.7 3880900 94.09 19109.0 9 1975 8.9 3900625 79.21 17577.5 10 1980 7.2 3920400 51.84 14256.0 TOTAL 1957 5 182. 9 3832012 5 4072.0 9 356816.5
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1. 9885 . ) 849 . 726 )( 5 . 2062 ( 25 . 1210 5 . 2062 10 ) 19575 ( 38320125 ) ( ) ( 849 . 726 25 . 1210 10 ) 9 . 182 ( 09 . 4072 10 ) 9 . 182 )( 19575 ( 5 . 356816 ) ( ) ( 2 2 2 2 2 2 - = - = = - = - = = - = - = - = - = - = = r r SS SS n x x SS SS SS SS SS n y y SS n y x y x SS SS SS SS r XX XX i i XX YY XY YY XY i i YY i i i i XY YY XX XY
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2. 5868 . 5 . 2062 25 . 1210 ˆ - = - = = + = b b SS SS b bx a y XX XY 951 . 1166 ) 5 . 1957 )( 5868 . ( 29 . 18 5 . 1957 10 19575 29 . 18 10 9 . 182 = - - = - = = = = = = = a a x b y a n x x n y y i i x y 5868 . 951 . 1166 ˆ - = (if you used x: 35, 40, 41, …,80: a =52.042)
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3. million 9962 . 8 ˆ ) 2004 ( 5868 . 951 . 1166 ˆ 2004 2004 - = - = y y This is bad, because 2004 is so much greater than any year in the data set; we extrapolated too far beyond the scope of the data and got a meaningless, unrealizable, number. 4. b in the equation in problem 2 says that, for every year increase in x, the population living on farms (y) decreases by .5868 million people. 5. Obs (i) X Y X 2 Y 2 XY 1 36 86 1296 7396 3096 2 48 90 2304
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